Fitch downgraded the credit rating of 18 Spanish banks, pointing to the weak economy and the banks' exposure to bad real estate loans. That came one day after the agency cut its rating on the nation's two largest banks, Santander (STD) and BBVA (BBVA).

Spain has requested up to 100 billion euros from the European Union to recapitalize insolvent banks. But the rescue plan failed to ease concerns about the Spanish government's ability to fund itself in the bond market.

The concern is that bailing out the banks will not solve the Spanish government's long-term debt problems. Indeed, many investors worry that Spain will eventually be forced to take a bailout similar to those provided for Greece, Portugal and Ireland.

Investors are also concerned that the cost of recapitalizing the banking sector will ultimately fall on the Spanish government.

"It now goes without saying that the challenges faced by the sovereign and banks in Spain are intrinsically linked," said Michael Symonds, a banking analyst at Daiwa Capital Markets.

The bailout plan has yet to be finalized and it remains to be seen how much money Madrid will need to clean up the banking sector. Fitch has estimated that the cost could reach 100 billion euros, while the International Monetary Fund said it would be at least 40 billion euros.

It's also unclear where the money will come from. Germany has called for the European Stability Facility to provide the capital, as opposed to the European Financial Stability Facility. The 500 billion euro ESM would be considered a preferred creditor, which means private sector bondholders would be effectively subordinated in any bailout of the Spanish government.

Meanwhile, investors are also concerned that the problems in Spain could spread to Italy. The yield on Italian 10-year bonds rose Tuesday to 6.15%.

Stamenkovic said the run-up in Spanish and Italian bond yields has raised speculation about an intervention by the European Central Bank. "The bailout for Spain has backfired and the markets are putting pressure on the ECB to do something," he said.

The ECB has purchased billions of euros worth of government debt under its Securities Market Program, which has been dormant for several weeks. It has also pumped over 1 trillion euros into the banking system by offering low-cost, long-term loans. The loans helped drive down borrowing costs for Spain and Italy as banks in those countries bought government debt.

Ben Rooney is a staff writer for CNNMoney. He covers the European debt crisis and other international finance stories, in addition to writing about stocks, bonds, investing and other Wall Street-related news. Follow Ben on Twitter: @ben_rooney